A motorist completes a journey of 1330 km in 14 hours what is his average speed in kilometres per hour? How long will it take to cover a distance of 570km at the same average speed... A motorist completes a journey of 1330 km in 14 hours what is his average speed in kilometres per hour? How long will it take to cover a distance of 570km at the same average speed?
Understand the Problem
The question has two parts: first, it asks to calculate the average speed of a motorist given the total distance traveled and the time taken. Second, it asks to calculate the time it would take to cover a different distance at the same average speed.
Answer
Average speed: $50$ mph Time to cover 225 miles: $4.5$ hours
Answer for screen readers
The average speed of the motorist is $50$ mph, and it would take $4.5$ hours to cover 225 miles at the same average speed.
Steps to Solve
- Calculate the average speed
To find the average speed, we divide the total distance by the total time.
Average speed $ = \frac{\text{Total distance}}{\text{Total time}} $ Given total distance $ = 150 $ miles and total time $ = 3 $ hours
Average speed $ = \frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ mph} $
- Calculate the time to cover 225 miles at the same average speed
To find the time it would take to cover 225 miles at the same average speed, we divide the new distance by the average speed.
Time $ = \frac{\text{Distance}}{\text{Average speed}} $ Given distance $ = 225 $ miles and average speed $ = 50 \text{ mph} $
Time $ = \frac{225 \text{ miles}}{50 \text{ mph}} = 4.5 \text{ hours} $
The average speed of the motorist is $50$ mph, and it would take $4.5$ hours to cover 225 miles at the same average speed.
More Information
The average speed is a scalar quantity, representing the distance traveled per unit of time. It is calculated by dividing the total distance traveled by the total time taken.
Tips
A common mistake is to confuse speed and time, and incorrectly divide time by distance instead of distance by time. Another mistake is failing to keep track of the units, which can lead to incorrect calculations.
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